Intellectual merit: Activity-regulated changes in synapse strength lie at the heart of molecular theories of learning and neural development. At glutamatergic synapses of the brain, regulation of receptor number is a core mechanism for rapidly changing synaptic strength. Multi-domain proteins of the postsynaptic density (PSD) bind receptors and regulate their trafficking, and this has lead to a model that these proteins serve as slots whose occupancy determines synaptic strength. However, direct tests of this model are lacking, and recent work suggests that it is incomplete. We have recently developed computational models to test the idea that the spatial distribution and mobility of proteins that make up the PSD may result in a phenomenon called macromolecular crowding. In such crowded spaces, the fundamental character of diffusion is altered such that receptors can be confined within very small (nanometer-sized) regions even without any need for binding to PSD-95 and similar scaffold molecules. High-resolution imaging studies of receptor diffusion in synapses, as well as light and electron microscopic imaging of synaptic proteins support such a view. Motivated by these observations, we hypothesize that macromolecular crowding in the PSD acts in concert with biochemical interactions to determine the number of synaptic receptors. Emerging computational models of diffusion and reaction in crowded spaces and state-of-the-art live-cell imaging will now allow us to test this hypothesis. To do so, we will: Specific Aim 1: Develop a structural model of core scaffold organization in the PSD. An interconnected set of scaffolding proteins forms the core of the PSD and is central to control of receptor numbers, but the distribution of proteins within the core, particularly in living synapses, remains undocumented. We will use super-resolution live-cell imaging to map the distribution of core proteins in the PSD. Then, incorporating structural, EM, and biochemical literature, we will elaborate and refine our published models to reproduce these measurements of PSD organization. Specific Aim 2: Develop a model of receptor mobility and lifetime in excitatory synapses. To extend this model so that it can account for receptor mobility, we will use high-throughput single-molecule tracking PALM and high-resolution photobleaching and photoactivation in synaptic subdomains to measure protein mobility within the synapse. Measurements of the intrasynaptic mobility of core scaffolds, and mobility of transmembrane membrane proteins or those resident in the external or internal membrane leaflets will provide model constraints. We will extend the model from Aim 1 to allow for measured characteristics using techniques developed to model physical systems such as colloids. Specific Aim 3: Test whether alterations in scaffold density, spacing, and mobility affect receptor mobility and receptor lifetime within the PSD. To test predictions of the model generated in Aim 2, we will use several molecular strategies to alter characteristics of the PSD core scaffold, and measure their influence on receptor mobility in cells. To alter crowding, we will alter spacing within the scaffold by engineering proteins with altered scaffold-linking domains. To control scaffold mobility, we will acutely cross-link targeted PSD constituents and use cytoskeletal inhibitors to arrest the internal dynamics of the PSD. Computer simulations of receptor diffusion using constraints derived above will be performed to extract mobility and lifetimes and compared to the measurements. Specific Aim 4: Test whether alterations of scaffold distribution and mobility in the PSD affect synaptic strength. The crowding effect can regulate the number or spatial arrangement of receptors, which are expected to affect receptor activation during neurotransmission. Using patch-clamp electrophysiology and glutamate photolysis, we will test whether synaptic efficacy changes in coordination with alterations of PSD crowding and scaffold mobility. Simulations of glutamate release will be used to test whether the reconstructed receptor mobility and distribution results in experimentally observed synaptic responses. Broader Impact: This work will greatly advance our fundamental understanding of synapse function and plasticity, thus also aiding research into synaptic dysfunction that underlies neuropsychiatric and neurodegenerative diseases. Second, this project, based on the synergy between theoretical sciences, novel computational methods, and new techniques in neurobiology, will provide a unique crossdisciplinary environment for training of young neuroscientists at Duke and Maryland. Finally, the project will be integrated into ongoing outreach efforts to expose local underrepresented high school and undergraduate students in Durham and Baltimore to advanced math and science.